Binary Operation

Let ∗ be a binary operation on the set M2(R) of all 2 × 2 matrices defined by∀A1, A2 ∈ M2(R), A ∗ B =1/2(AB-BA)
(a) Prove that the operation is binary.(b) Determine whether the operation is associative and/or commutative.

I think its a binary operation because R X R = R.
But, I am unable to prove the second part.

Re: Binary Operation

Originally Posted by abhistud

Let ∗ be a binary operation on the set M2(R) of all 2 × 2 matrices defined by∀A1, A2 ∈ M2(R), A ∗ B =1/2(AB-BA)
(a) Prove that the operation is binary.(b) Determine whether the operation is associative and/or commutative.
I think its a binary operation because R X R = R.
But, I am unable to prove the second part.